1. The problem is to simplify the expression $\frac{1}{i^2}$.\n\n2. Recall that $i$ is the imaginary unit, defined by $i^2 = -1$.\n\n3. Substitute $i^2$ with $-1$ in the expression:\n$$\frac{1}{i^2} = \frac{1}{-1}$$\n\n4. Simplify the fraction:\n$$\frac{1}{-1} = -1$$\n\n5. Therefore, the simplified value of $\frac{1}{i^2}$ is $-1$.